derivative of 460(1+x/(x^2+80))

解

\frac{d}{d x} (460 (1 + \frac{x}{x ^{2} + 80}))

\frac{460 ( - x ^{2} + 80 )}{( x ^{2} + 80 ) ^{2}}

解答ステップ

\frac{d}{d x} (460 (1 + \frac{x}{x ^{2} + 80}))

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 460 \frac{d}{d x} (1 + \frac{x}{x ^{2} + 80})

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 460 (\frac{d}{d x} (1) + \frac{d}{d x} (\frac{x}{x ^{2} + 80}))

\frac{d}{d x} (1) = 0

\frac{d}{d x} (\frac{x}{x ^{2} + 80}) = \frac{- x ^{2} + 80}{( x ^{2} + 80 ) ^{2}}

= 460 (0 + \frac{- x ^{2} + 80}{( x ^{2} + 80 ) ^{2}})

簡素化

460 (0 + \frac{- x ^{2} + 80}{( x ^{2} + 80 ) ^{2}}) : \frac{460 ( - x ^{2} + 80 )}{( x ^{2} + 80 ) ^{2}}

= \frac{460 ( - x ^{2} + 80 )}{( x ^{2} + 80 ) ^{2}}